TAMPA, Fla.—James Dimon tightened his grip on the nation's largest bank on Tuesday as shareholders of J.P. Morgan Chase & Co. overwhelmingly endorsed his dual role as chairman and chief executive.

A year after a multibillion-dollar trading fiasco tainted Mr. Dimon's reputation as Wall Street's best risk manager, just 32.2% of shareholders voted for a resolution to split the two positions. That was well below the 40.1% who voted...